Overlay and Semiconductor Process Control Using a Wafer Geometry Metric

ABSTRACT

The present invention may include acquiring a wafer shape value at a plurality of points of a wafer surface at a first and second process level, generating a wafer shape change value at each of the points, generating a set of slope of shape change values at each of the points, calculating a set of process tool correctables utilizing the generated set of slope of shape change values, generating a set of slope shape change residuals (SSCRs) by calculating a slope of shape change residual value at each of the points utilizing the set of process tool correctables, defining a plurality of metric analysis regions distributed across the surface, and then generating one or more residual slope shape change metrics for each metric analysis region based on one or more SSCRs within each metric analysis region.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is related to and claims the benefit of theearliest available effective filing date(s) from the following listedapplication(s) (the “Related Applications”) (e.g., claims earliestavailable priority dates for other than provisional patent applicationsor claims benefits under 35 USC §119(e) for provisional patentapplications, for any and all parent, grandparent, great-grandparent,etc. applications of the Related Application(s)).

RELATED APPLICATIONS

-   -   For purposes of the USPTO extra-statutory requirements, the        present application constitutes a continuation patent        application of United States patent application entitled OVERLAY        AND SEMICONDUCTOR PROCESS CONTROL USING A WAFER GEOMETRY METRIC,        naming Pradeep Vukkadala, Sathish Veeraraghavan, and Jaydeep K.        Sinha as inventors, filed May 21, 2012, application Ser. No.        13/476,328, which constitutes a regular (non-provisional) patent        application of U.S. Provisional Patent Application entitled        OVERLAY AND SEMICONDUCTOR PROCESS CONTROL USING A NOVEL WAFER        GEOMETRY METRIC, naming Sathish Veeraraghavan, Pradeep        Vukkadala, and Jaydeep K. Sinha as inventor, filed Oct. 11,        2011, Application Ser. No. 61/545,942. All of the patent        applications listed above are incorporated herein by reference        in the entirety.

TECHNICAL FIELD

The present invention generally relates to a method and system forproviding a wafer geometry metric, and, a method and system forproviding a wafer geometry metric suitable for allowing improved overlayand process control during semiconductor fabrication.

BACKGROUND

Fabricating semiconductor devices such as logic and memory devicestypically includes processing a substrate such as a semiconductor waferusing a large number of semiconductor fabrication processes to formvarious features and multiple levels of the semiconductor devices. Forexample, lithography is a semiconductor fabrication process thatinvolves transferring a pattern from a reticle to a resist arranged on asemiconductor wafer. Additional examples of semiconductor fabricationprocesses include, but are not limited to, chemical-mechanical polishing(CMP), rapid thermal processing (RTP), etching, deposition, and ionimplantation. Multiple semiconductor devices may be fabricated in anarrangement on a single semiconductor wafer and then separated intoindividual semiconductor devices.

Due to the ever shrinking integrated circuit node sizes, thecharacterization of semiconductor wafer geometry has become increasinglyimportant. Wafer geometry has traditionally been classified withparameters that vary at low frequency across a given wafer. Suchcharacteristics may include shape and/or flatness. Shape is typicallydefined as the deviation of the median surface of a wafer from areference plane, and is quantified using a global metric, such as warpor bow. Flatness is defined as the thickness variation of a substratewith the back surface assumed to be completely flat, and ischaracterized by site-based metrics such as SFQR (site front surfaceleast square fit plane range).

Shape characterization is performed using methods that measure largevariations across an entire surface of a wafer. In addition to the lowfrequency components of wafer shape it is advantageous to quantify thehigher order components of shape, which are limited to localized regionsof the substrate, and generally cannot be characteristic satisfactorilyusing a global shape metric, such as warp and bow. With increased demandon defocus and overlay budgets, the importance of high order shapecharacterization continues to increase. In addition, the application ofsemiconductor processes to a wafer may impact wafer topography, such aswafer shape. These changes in wafer shape lead to in-plane as well asout-of-plane distortions of the wafer.

An overlay measurement generally specifies how accurately a firstpatterned layer aligns with respect to a second patterned layer disposedabove or below it or how accurately a first pattern aligns with respectto a second pattern disposed on the same layer. Overlay error istraditionally determined with an overlay target having structures formedon one or more layers of a semiconductor wafer. If the two layers orpatterns are properly formed, then the structure on one layer or patterntends to be aligned relative to the structure on the other layer orpattern. If the two layers or patterns are not properly formed, then thestructure on one layer or pattern tends to be offset or misalignedrelative to the structure on the other layer or pattern. Overlay erroris the misalignment between any of the patterns used at different stagesof semiconductor integrated circuit manufacturing.

The in-plane distortions created by changes in wafer shape result in amisregistration between features in sequential patterning steps, whichare manifest in measured overlay error between the patterned layers. Assuch, there is a need for improved wafer shape and wafer shape changecharacterization. As such, it is advantageous to provide a method andsystem that remedies these identified deficiencies.

SUMMARY

A method for providing a wafer geometry metric is disclosed. In oneaspect, a method may include, but is not limited to, acquiring a wafershape value at each of a plurality of points of a surface of a wafer ata first process level and an additional process level; generating awafer shape change value at each of the points utilizing the acquiredwafer shape value at each of the points at the first process level andthe additional process level, the wafer shape change value at each pointcorresponding to a change in wafer shape between the first process leveland the second process level; generating a set of slope of shape changevalues by calculating a slope of shape change at each of the pointsutilizing the generated wafer shape change value at each of the points,each of the slope of shape change values corresponding to a slope of thechange in wafer shape along at least one direction of the surface of thewafer; calculating a set of process tool correctables utilizing thegenerated set of slope of shape change values; generating a set of slopeshape change residuals (SSCRs) by calculating a slope of shape changeresidual value at each of the points utilizing the set of process toolcorrectables; defining a plurality of metric analysis regionsdistributed across the surface of the wafer, each metric analysis regionencompassing one or more points of the plurality of points; andgenerating one or more residual slope shape change metrics for eachmetric analysis region based on one or more SSCRs within each metricanalysis region.

In another aspect, a method may include, but is not limited to,acquiring a wafer shape value at each of a plurality of points of asurface of the wafer at a process level; generating a set of slope ofshape values by calculating a slope of shape value at each of the pointsat the process level utilizing the wafer shape values acquired at theprocess level; calculating a set of process tool correctables utilizingthe generated set of slope of shape values; generating a set of slopeshape residuals (SSRs) by calculating a slope of shape residual value ateach of the points utilizing the set of process tool correctables;defining a plurality of metric analysis regions distributed across thesurface of the substrate, each metric analysis region encompassing oneor more points of the plurality of points; and generating one or moreresidual slope shape metrics for each metric analysis region based onone or more SSRs within each metric analysis region.

A method for sorting wafers utilizing a slope of shape metric isdisclosed. The method may include, but is not limited to, receiving aplurality of wafers; acquiring a set of wafer shape values from asurface of each wafer at a selected process level; generating a set ofresidual slope shape metrics for each wafer by calculating a residualslope shape metric at each of a plurality of points of each wafer;determining a neutral surface of each wafer in a chucked state;calculating a neutral surface factor (NSF) for each wafer utilizing thedetermined neutral surface for each wafer and a plurality of positionsassociated with a plurality of patterns of each wafer; determining a setof pattern placement error (PPE) residual values for each wafer, the PPEresidual value for each point for each wafer being a product of at leastthe calculated NSF for each wafer, the residual slope shape metric forthe point, and a thickness of the wafer; determining one or morethresholds for the set of residual shape metrics suitable formaintaining the set of PPE residuals below one or more selected levels;and characterizing the plurality of wafers by comparing the determinedone or more thresholds for the set of residual shape metrics to thegenerated set of residual slope shape metrics for each wafer.

A method for process uniformity control is disclosed. The method mayinclude, but is not limited to, acquiring a wafer shape value at each ofa plurality of points of a surface of a wafer at a first process leveland an additional process level; generating a wafer shape change valueat each of the points utilizing the acquired wafer shape value at eachof the points at the first process level and the additional processlevel, the wafer shape change value at each point corresponding to achange in wafer shape between the first process level and the secondprocess level; generating one or more residual slope shape changemetrics utilizing the generated wafer shape change value at each of thepoints; and providing process control to one or more process tools basedon the generated one or more residual slope shape change metrics.

A method for overlay control is disclosed. The method may include, butis not limited to, acquiring a wafer shape value at each of a pluralityof points of a surface of a wafer at a first process level and anadditional process level; generating a set of wafer shape change valuesby calculating a wafer shape change value at each of the pointsutilizing the acquired wafer shape value at each of the points at thefirst process level and the additional process level; generating a setof slope shape change residuals utilizing the generated wafer shapechange value at each of the points; calculating a set of residual slopeshape change metrics utilizing the set of sloe shape change residuals;acquiring a set of overlay values at a plurality of points on thesurface of the wafer at the additional process level, the set of overlayvalues associated with a misalignment produced between the first processlevel and the additional process level; generating a set of overlayresiduals utilizing the acquired set of overlay values; calculating aset of overlay residual metrics utilizing the set of overlay residuals;generating a calibration curve by comparing the set of residual slopeshape change metrics to the set of residual overlay metrics; anddetermining a threshold for the set of residual slope shape changemetrics suitable for maintaining residual overlay below a selected levelbased on the generated calibration curve.

A system for providing a wafer geometry metric is disclosed. In oneaspect, a system may include, but is not limited to, a topography systemconfigured to perform a set of topography measurements in order toacquire a wafer shape value at each of a plurality of points of asurface of a wafer at a first process level and an additional processlevel; and one or more computing systems communicatively coupled to thetopography and configured to receive the set of topography measurements,the one or more computing systems further configured to: generate awafer shape change value at each of the points utilizing the acquiredwafer shape value at each of the points at the first process level andthe additional process level; generate a set of slope of shape changevalues by calculating a slope of shape change at each of the pointsutilizing the generated wafer shape change value at each of the points;calculating a set of process tool correctables utilizing the generatedset of slope of shape change values; generating a set of slope shapechange residuals (SSCRs) by calculating a slope of shape change residualvalue at each of the points utilizing the set of process toolcorrectables; defining a plurality of metric analysis regionsdistributed across the surface of the substrate; and generating one ormore residual slope shape change metrics for each metric analysis regionbased on one or more SSCRs within each metric analysis region.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not necessarily restrictive of the invention as claimed. Theaccompanying drawings, which are incorporated in and constitute a partof the specification, illustrate embodiments of the invention andtogether with the general description, serve to explain the principlesof the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the disclosure may be better understood bythose skilled in the art by reference to the accompanying figures inwhich:

FIG. 1 illustrates a conceptual view of wafer shape change inducedoverlay error, in accordance with the present invention.

FIG. 2A illustrates a block diagram view of a system for providing awafer metric, in accordance with the present invention.

FIG. 2B illustrates a schematic view of dual Fizeau cavity of a dualFizeau interferometer, in accordance with the present invention.

FIG. 3A illustrates a functional block diagram of wafer geometry metricgeneration, in accordance with the present invention.

FIG. 3B illustrates a functional block diagram of residual slope ofshape change metric calculation using process tool correctables, inaccordance with the present invention.

FIG. 3C illustrates a functional block diagram of wafer geometry metricgeneration, in accordance with the present invention.

FIG. 4 illustrates a functional block diagram of wafer sorting utilizinga wafer geometry metric, in accordance with the present invention.

FIG. 5 illustrates a functional block diagram of process feedbackcontrol utilizing a wafer geometry metric, in accordance with thepresent invention.

FIG. 6 illustrates a functional block diagram of overlay controlutilizing a wafer geometry metric, in accordance with the presentinvention.

FIG. 7 illustrates a process flow diagram for providing a wafer metric,in accordance with the present invention.

FIG. 8 illustrates a process flow diagram for providing a wafer metric,in accordance with the present invention.

FIG. 9A illustrates a process flow diagram for sorting a plurality ofwafers utilizing a wafer geometry metric, in accordance with the presentinvention.

FIG. 9B illustrates a conceptual view of a neutral surface and neutralsurface factor (NSF) of a wafer, in accordance with the presentinvention.

FIG. 10 illustrates a process flow diagram for process control utilizinga wafer geometry metric, in accordance with the present invention.

FIG. 11 illustrates a process flow diagram for overlay control utilizinga wafer geometry metric, in accordance with the present invention.

FIG. 12 illustrates an overlay residual and slope of shape changeresidual calibration curve, in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the subject matter disclosed,which is illustrated in the accompanying drawings.

Referring generally to FIGS. 1A through 12, a system and method forproviding a wafer geometry metric is described in accordance with thepresent disclosure. The present invention is directed to a method andsystem for providing one or more wafer geometry metrics derived fromwafer shape data acquired using a semiconductor wafer topographytechnique (e.g., Fizeau interferometry). In this regard, the variousembodiments of the present invention may act to quantify wafer shape ata selected process level or the change in wafer shape between a firstprocess level (e.g., bare ware level) and an additional process level.In one aspect, the present invention may utilize these wafer shapemeasurements to provide a set of “slope of wafer shape change” data. Inan alternative aspect, the present invention may also provide a set of“slope of shape” data, derived from wafer shape measurements. Utilizingthe slope of wafer shape change (referred to herein as “slope shapechange”) data and/or the slope of shape (referred to herein as “slopeshape”) data along with one or more process tool correctables routines,a variety of geometry wafer metrics may be generated. The generatedwafer metrics may in turn be used to provide a number of improvedfabrication and process control techniques. The present invention isfurther directed to i) a method and system for sorting wafers; ii) amethod and system for process uniformity control; and iii) a method andsystem for overlay control.

As used throughout the present disclosure, the term “wafer” generallyrefers to a substrate formed of a semiconductor or non-semiconductormaterial. For example, a semiconductor or non-semiconductor material mayinclude, but is not limited to, monocrystalline silicon, galliumarsenide, and indium phosphide. A wafer may include one or more layers.For instance, such layers may include, but are not limited to, a resist,a dielectric material, a conductive material, and a semiconductivematerial. Many different types of such layers are known in the art, andthe term wafer as used herein is intended to encompass a wafer on whichall types of such layers may be formed.

A typical semiconductor process includes wafer processing by lot. Asused herein a “lot” is a group of wafers (e.g., group of 25 wafers)which are processed together. Each wafer in the lot is comprised of manyexposure fields from the lithography processing tools (e.g. steppers,scanners, etc.). Within each field may exist multiple die. A die is thefunctional unit which eventually becomes a single chip. One or morelayers formed on a wafer may be patterned or unpatterned. For example, awafer may include a plurality of dies, each having repeatable patternedfeatures. Formation and processing of such layers of material mayultimately result in completed devices. Many different types of devicesmay be formed on a wafer, and the term wafer as used herein is intendedto encompass a wafer on which any type of device known in the art isbeing fabricated.

Throughout the present disclosure, “shape” is defined as the mediansurface of a wafer (or substrate) as generally measured in a free state.Typically, shape is characterized by a global metric, such as warp orbow. In addition, higher order components of shape may be calculated.Higher order components of wafer shape, which are associated withlocalized areas of the wafer, typically, do not impact global shapemetrics. Higher order shape (HOS) may be quantified utilizing ashape-slope metric, which is a measure of the change of the shape as afunction of position across the wafer. The utilization of shape-slope tomeasure high order shape is discussed in detail in U.S. Pat. No.8,065,109 by Veeraraghavan et al., entitled Localized Substrate GeometryCharacterization, issued on Nov. 22, 2011, which is incorporated hereinby reference.

FIG. 1 illustrates a conceptual view of wafer shape distortion inducedoverlay error. Wafer shape change resulting from wafer processing and/orwafer chucking may induce in-plane distortions (IPD) within the wafer,which may lead to overlay error between a first patterning step (N) anda subsequent patterning step (N+1). It should be recognized by thoseskilled in the art that a wafer chucking procedure may act to flattenthe back-side of the wafer, as shown between step 102 and 104 of FIG. 1,resulting in the which results in bending and shear deformation of thewafer. It is noted herein that wafer processing may include any waferprocessing technique known in the art, such as, but not limited to, CMP,RTP, etching, and film deposition. As shown in FIG. 1, an initial wafermay be received in a free state at patterning step N (step 102). In theinitial free state, the wafer may have a characteristic length between aset of patterns of L. Then, the wafer may be chucked and features may bepatterned on the wafer (step 104). The chucking and patterning step Nproduce a change in the characteristic length of ΔL_(N). This results inan overall length between the patterned features of L+ΔL_(N). Then, thewafer may undergo a post film deposition process (step 106), which mayact to change the shape of the wafer. Next, the wafer may undergo asubsequent patterning step N+1 while in a chucked state (step 108). Thesecond chucking and N+1 patterning step may produce an additional changein characteristic length of ΔL_(N+1), yielding an overall length ofL+ΔL_(N)+ΔL_(N+1). Due to the wafer shape change that occurs betweensteps N and N+1, the elastic distortion of the wafer that occurs duringchucking in patterning step N is different from the distortion thatoccurs during chucking in patterning step N+1. The correspondingdifference in in-plane distortions during chucking at the differentsteps may then manifest as overlay errors between the N and N+1patterns. The relationship between wafer shape change and overlay erroris described in detail in K. Turner et al, “Predicting Distortions andOverlay Errors Due to Wafer Deformation During Chucking on LithographyScanners”, J. Micro/Nanolith, MEMS MOEMS 8(4), 043015, (October-December2009), which is incorporated in the entirety herein by reference. Inaddition, chucking induced wafer shape change and in-plane distortionsare described generally in U.S. patent application Ser. No. 12/778,013by Veeraraghavan et al., entitled Site Based Quantification of SubstrateTopography and Its Relation to Lithography Defocus and Overlay, filed onMay 11, 2010, which is incorporated in the entirety herein by reference.

FIGS. 2A-2B illustrate a system 200 for providing a wafer geometrymetric, in accordance with one embodiment of the present invention. Inone aspect, the system 200 may include a topography measurement system202 configured to perform one or more topographic measurements of awafer 204. In one embodiment, the topography measurement system 202 mayinclude a Dual Fizeau interferometer 220 suitable for simultaneouslymeasuring topography of the front-side of the wafer 204 and theback-side of the wafer 204. In another aspect, the system 200 mayinclude one or more computing systems 206 communicatively coupled to thetopographic measurement system 202 and configured to receive topographymeasurements from the measurement system 202.

FIG. 2B illustrates a conceptual view of a Dual Fizeau cavity inaccordance with the present invention. As shown in FIG. 2B, the DualFizeau cavity may be configured to hold the wafer 204 in a substantiallyvertical position. For instance, the Dual Fizeau cavity 216 many includea set of point contact devices (not shown) configured to receive andhold the wafer in a substantially upright position in a substantiallyfree state. Utilizing the two reference flats 218 a and 218 b, whichserve as the reference surfaces for the interferometer, the Dual Fizeauinterferometer may analyze various parameters associated with the wafer204 and its spatial relationship to the reference flats 218 a and 218 b.

Utilizing the Dual Fizeau interferometer 220, the topography system 202may simultaneously measure height variations of both the front-sidesurface and back-side surface of the wafer 204. The shape value at eachof the measured points of the front-side and/or back-side surface maythen be calculated utilizing the measured height variation at thosepoints. The shape, s(x,y), of the wafer as a function of X-Y position onthe surface of the wafer may be expressed as:

$\begin{matrix}{{s( {x,y} )} \approx {{\frac{1}{2}( {{d_{A}( {x,y} )} - {d_{B}( {x,y} )}} )} - {Tilt}}} & ( {{Eq}.\mspace{14mu} 1} )\end{matrix}$

where d_(A)(x,y) represents the cavity distance between the referenceflat A 228 a of cavity 226 and a first side 230 (e.g., front-side) ofthe wafer, d_(B)(x,y) represents the cavity distance between thereference flat B 228 b of cavity 226 and a second side 232 (e.g.,back-side) of the wafer, Tilt represents the tilt of the wafer 202within the Dual Fizeau cavity 226. Utilizing the relationship of Eq. 1 atwo-dimensional X-Y map of shape may be constructed by calculating shapeat a plurality of positions on the wafer 204. For example, a shape maphaving a lateral resolution of approximately 500 μm may be constructedutilizing the height variation measurements acquired with theinterferometry system 220 and the corresponding shape value at each ofthe measured points on the wafer. In a further embodiment, the one ormore computing systems 206 may execute a preprogrammed algorithmconfigured to compute shape at the plurality of selected measurementpoints by applying a shape calculating algorithm (e.g., equation 1) tointerferometry data received from the topography system 202. Dual Fizeauinterferometry suitable for measuring front-side and back-sidetopography of a wafer is described in detail in Klaus Freischlad et al.,“Interferometry for Wafer Dimensional Metrology”, Proc. SPIE 6672, 1(2007), which is incorporated in the entirety herein by reference. Inaddition, Dual sided interferometry is described generally in U.S. Pat.No. 6,847,458 by Freischlad et al., entitled Method and Apparatus forMeasuring the Sahpe and Thickness Variation of Polished Opaque Plates,issued on Jan. 25, 2005, U.S. Pat. No. 8,068,234 by Tang et al.,entitled Method and Apparatus for Measuring Shape or ThicknessInformation of a Substrate, issued on Nov. 29, 2011, which are bothincorporated in the entirety herein by reference.

In a further embodiment, the topography system 202 may be configured toaccept instructions from another subsystem of the system 200 in order tocarry out a designated measurement scheme. For instance, the topographysystem 202 may accept instructions from one or more computing systems206 of the system 200. Upon receiving the instructions from thecomputing system 206, the topography system 202 may perform topographicmeasurements (i.e., wafer geometry measurements) at various locations,or points, across one or more surfaces (e.g., front-side surface orback-side surface) of the semiconductor wafer 204 identified in theprovided instructions.

In another aspect, the one or more computing systems 206 may beconfigured to receive a set of measurements performed by the topographysystem 202 in a sampling process of one or more wafers of a lot. Uponreceiving results of the one or more sampling process from thetopography system 202, the one or more computing systems 206 may thengenerate one or more wafer geometry metrics (e.g., slope shape changemetric or slope shape metric) via a preprogrammed wafer geometry metricalgorithm 211, discussed further herein. In additional embodiments, thesystem 200 may utilize the geometry metric for a variety of processcontrol features. For example, the system 200 may further be configuredto execute a wafer sorting algorithm 212, a process control algorithm213, and/or an overlay correction algorithm 215.

FIG. 3A illustrates a high-level functional block diagram 300 depictingthe generation of one or more slope shape change wafer geometry metricsutilizing a wafer geometry metric algorithm 211 in accordance with oneembodiment of the present invention. The topography system 202 mayperform a set of shape measurements 302 for both a first process leveland an additional process level. The processes levels may include anyprocess level in a semiconductor wafer fabrication process. For example,the process levels (i.e., the first process level or the additionalprocess level) may include any one of bare-wafer processing,chemical-mechanical planarization (CMP), rapid thermal processing (RTP),etching, film deposition, and the like.

Next, the computing system 206 of the system 200 may receive themeasurements 302 for the first process level (e.g., level N) and theadditional process level (e.g., level N+1) and calculate the slope ofshape change between the first process level and the additional processlevel in the X- and Y-direction 304. Following the slope of shape changecalculation, a set of process tool (e.g., scanner) correctables (e.g.,linear correctables or higher-order correctables) may be calculated bythe computing system 206 and fed to a communicatively coupled processtool (not shown) for correction. Next, residual slope of shape changevalues for both the X-direction and Y-direction may be calculated 308.Utilizing the calculated residual slope of shape change values 308 thecomputing system 206 may further generate a global slope shape changemetric 310, a set of local slope shape change metrics 312 and/or aresidual slope shape change contour map 314.

In a further embodiment, the wafer geometry metric algorithm 211 maycalculate wafer-level or field-level process tool correctables. FIG. 3Billustrates a high-level functional block diagram depicting thecalculation of process tool correctables 317, in accordance with oneembodiment of the present invention. Following the slope of shape changecalculation 304, the computing system 206 may calculate eitherwafer-level or field-level correctables. In the case of wafer-levelcorrections, the computing system 206 may calculate correctables, at awafer level, based on a selected process tool correction routinesuitable for calculating the residual overlay. Then, using thesecorrectables the computing system 206 may calculate the residual slopeof shape change in the X-direction and the Y-direction 324. In the caseof field-level corrections, the user or a user controlled sub-system mayselect a field size. Then, the computing system 206 may calculatecorrectables, at a field-level, based on a selected process toolcorrection routine suitable for calculating the residual overlay.

In turn, using these correctables the computing system 206 may calculatethe residual slope of shape change in the X-direction and theY-direction 308. In a further aspect, the computing system 206 may thencalculate one or more global metrics 310 and/or one or more localmetrics 312. In addition, utilizing the calculated set of slope of shapechange residuals 308, the computing system 206 may generate a contourmap 314 depicting the slope of shape change residuals as a function ofposition on a two-dimensional grid. This map 314 may then be presentedto a user via a display device (not shown). The computing system 206 mayfurther be configured to receive input from a user interface device(e.g., mouse, keyboard, trackpad, touchscreen, and the like) allowing auser to “tag” or identify regions of interest on the contour map 314displayed via the display device.

FIG. 3C illustrates a high-level functional block diagram 350 depictingthe generation of one or more slope shape wafer geometry metricsutilizing an alternative embodiment of the wafer geometry metricalgorithm 211, in accordance with an alternative embodiment of thepresent invention. The system 200 may perform a set of shapemeasurements 352 of a wafer at a selected process level (e.g., abare-wafer process). Then, the computing system 206 of the system mayreceive these measurements and calculate the slope of shape in the X-and Y-direction 354. Following the slope of shape calculation, a set ofprocess tool (e.g., scanner) correctables (e.g., linear correctables orhigher-order correctables) may be calculated by the computing system 206and fed to a communicatively coupled process tool (not shown) forcorrection. Next, residual slope of shape values for both the X- andY-direction may be calculated 358. Utilizing the calculated residualslope of shape values 358 the computing system 206 may further generatea global slope shape metric 360, a set of local slope shape metrics 362and/or a two-dimensional residual slope shape map 364. It is furthernoted that the residual slope shape is calculated from the process toolcorrectables in a manner similar to that depicted in FIG. 3B and,therefore, the description of FIG. 3B should be interpreted to extend toFIG. 3C. It is further noted that details related to the generation ofone or more slope shape wafer geometry metrics and one or more slopeshape change metrics are described in greater detail further herein.

FIG. 4 illustrates a high-level functional block diagram 400 depictingthe sorting of wafers utilizing a wafer sorting algorithm 212. In oneaspect, the system 200 may sort a group of wafers utilizing a slope ofshape metric as described previously with respect to FIG. 3C. The system200 may acquire a set of wafer shape values via a set of topographymeasurements 404 from each of a group of wafers 402 at a selectedprocess level (e.g., bare wafer process level). It is noted that thewafer shape values may be acquired in one of the various mannersdescribed throughout the present invention. Then, the computing system206 may calculate a set of residual slope shape metrics 406 for each ofthe wafers 402. The calculation of each of the residual slope shapemetrics may be carried out in a manner similar to that describedpreviously herein, and which will be described in greater detail furtherherein. Next, the system 200 may determine a set of pattern placementerror (PPE) residual values utilizing an analytical residual PPE model408. In determining the set of PPE residual values, the system 200 maydetermine a neutral surface of the wafer in a chucked state and thencalculate a neutral surface factor (NSF) for each wafer utilizing theneutral surface for each wafer and a set of positions associated with aset of patterns of each wafer. Applicant notes that the concept ofneutral surface and neutral surface factor will be described in greaterdetail further herein. The set of pattern placement error (PPE) residualvalues may be calculated for each wafer. In this regard, a PPE residualvalue for each measured point of each wafer may be calculated bydetermining the product of at least the calculated NSF for each wafer,the residual slope shape metric for the point, and a thickness of thewafer. In turn, a threshold 410, or “specification,” for the set ofresidual shape metrics may be found that maintains the set of PPEresiduals below a selected level. Then, the group of wafers may besorted 412 based on the measured residual shape slope 406 of each waferand the threshold 410 required to maintain PPE residuals below aselected level (selected level determined by requirements of specificprocess or technology). It is noted herein that wafer sorting in thecontext of the present invention is described in greater detail furtherherein.

FIG. 5 illustrates a high-level functional block diagram 500 depictingprocess control utilizing a process control algorithm 213, in accordancewith one embodiment of the present invention. The topography system 202may perform a set of shape measurements for both a first process level502 and an additional process level 506. The computing system 206 of thesystem 200 may receive the measurements 502 and 506 for the firstprocess level (e.g., level N) and the additional process level (e.g.,level N+1) and calculate the slope of shape change 508 (e.g., front-sideslope of shape change or back-side slope of shape change) associatedwith the process 504 between the first process level and the additionalprocess level in the X- and Y-direction. Following the slope of shapechange calculation, residual slope of shape change values for both theX-direction and Y-direction may be determined. Utilizing the residualslope of shape change values the computing system 206 may furthergenerate one or more slope shape change metrics 510. It is noted hereinthat the slope shape change metrics 510 may be generated in any of thevarious manners discussed throughout the present disclosure. Then, basedon the generated wafer slope shape change metrics 510, the system 200may provide feedback to the process tool, thereby providing processcontrol to the one or more process tools. The process tools may includeany process tools known in the art, such as, but not limited to a RTPsystem, a film deposition system, a CMP system, and an etching system.

FIG. 6 illustrates a high-level function block diagram 600 depictingoverlay control utilizing an overlay control algorithm 215, inaccordance with one embodiment of the present invention. The topographysystem 202 may perform a set of shape measurements on a wafer at a firstprocess level 604 and then an additional process level 612, following aseries of processes (e.g., first process 606, second process 608, and upto and include an Nth process 610) between a first patterning step 602and a second patterning step 614. The computing system 206 of the system200 may receive the measurements 604 and 612 for the first process level(e.g., level N) and the additional process level (e.g., level N+1) andcalculate the slope of shape change 616 (e.g., front-side slope of shapechange or back-side slope of shape change) associated with the processsteps 606, 608, and 610 between the first process level 604 and theadditional process level 612 in the X- and Y-direction. Following theslope of shape change calculation, residual slope of shape change valuesand residual slope of shape change metrics 622 for both the X-directionand Y-direction may be determined. It is noted herein that the residualslope shape change and the associated residual slope shape changemetrics 622 may be generated in any of the various manners discussedthroughout the present disclosure. In addition, the system 200 mayacquire a set of overlay values 616 from a plurality of measurementpoints on the surface of the wafer at the additional process level(i.e., the process level following the selected N-number of processesbeing analyzed). For example, the system 200 may include an overlaymetrology tool (not shown) that is configured to perform overlaymetrology on a set of metrology targets of the wafer. In turn, theseoverlay metrology measurements may be transmitted to the computingsystem 206, whereby the computing system 206 may generate a set ofoverlay residuals and a set of corresponding overlay residual metrics618. It is recognized that the calculation of overlay residuals may beperformed in any manner known in the art (e.g., linear methodology orhigher-order methodology). It is further recognized that the overlayresidual metrics 618 may be generated in any of the various mannersdiscussed throughout the present disclosure.

Next, the computing system 206 may utilize the calculated set of slopeshape change residual metrics and the calculated set of overlay residualmetrics to form a calibration curve for the given one or more analyzedprocesses, process 1 through process N. The calibration curve isconfigured to relate the set of overlay residuals (or overlay residualmetrics) to the set of wafer slope shape change residuals (or waferslope shape change metrics). Applicant notes that the generation of thecalibration curve will be described in more detailed further herein.Based on the calibration curve a residual slope shape change thresholdmay be found that is suitable for maintaining residual overlay below aselected level (e.g., specification below a selected distance). Thecomputing system 206 may further sort a group of wafers by generating aset of residual slope shape change metrics for each of the wafer andthen comparing the acquired set of residual slope shape change metricsto the determined threshold. Utilizing this process the system 200 mayact to sort wafers to meet lithography overlay residual processspecifications by monitoring wafer slope shape change metrics.

It should be recognized that the various steps described throughout thepresent disclosure may be carried out by a single computer system or,alternatively, a multiple computer system. Moreover, differentsubsystems of the system 200, such as topography system 202, may includea computer system suitable for carrying out at least a portion of thesteps described above. Therefore, the above description should not beinterpreted as a limitation on the present invention but merely anillustration. Further, the one or more computing systems 206 may beconfigured to perform any other step(s) of any of the method embodimentsdescribed herein. In another embodiment, the computer system 206 may becommunicatively coupled to the topography system 202 or a process tool(not shown) in any manner known in the art. For example, the one or morecomputer systems 206 may be coupled to a computer system of thetopography system 202 or to a computer system of a process tool. Inanother example, the topography system 202 and a process tool may becontrolled by a single computer system. In this manner, the computersystem 206 of the system 200 may be coupled to a singletopography-process tool computer system. Moreover, the computer system206 of the system 200 may be configured to receive and/or acquire dataor information from other systems (e.g., inspection results from aninspection system, metrology results from an additional metrologysystem, or process tool correctables calculated from a system, such asKLA-Tencor's KT Analyzer) by a transmission medium that may includewireline and/or wireless portions. In this manner, the transmissionmedium may serve as a data link between the computer system 206 andother subsystems of the system 200. Moreover, the computer system 206may send data to external systems via a transmission medium.

The computing system 206 may include, but is not limited to, a personalcomputer system, mainframe computer system, workstation, image computer,parallel processor, or any other device known in the art. In general,the term “computing system” may be broadly defined to encompass anydevice having one or more processors, which execute instructions from amemory medium. Program instructions 208 implementing methods such asthose described herein may be transmitted over or stored on carriermedium 210. The carrier medium may be a transmission medium such as awire, cable, or wireless transmission link. The carrier medium may alsoinclude a storage medium such as a read-only memory, a random accessmemory, a magnetic or optical disk, a magnetic tape, or the like.

The embodiments of the system 200 illustrated in FIG. 2 may be furtherconfigured as described herein. In addition, the system 200 may beconfigured to perform any other step(s) of any of the methodembodiment(s) described herein.

FIG. 7 illustrates a process 700 for providing a wafer geometry metricsuitable for implementation by the system 200 of the present invention.In one aspect, it is recognized that data processing steps of theprocess flow 700 may be carried out via a pre-programmed algorithmexecuted by one or more processors of the one or more computing systems206. While the following description is presented in the context ofsystem 200, it is recognized herein that the particular structuralaspects of system 200 do not represent limitations and should beinterpreted as illustrative only.

In step 702, a wafer shape value at each of a plurality of points of asurface of a wafer maybe acquired at a first process level and a secondprocess level. In one embodiment, a set of wafer shape valuescorresponding to a selected number of measurement points on a surface ofa wafer 204 may be acquired using a topography measurement system 202.In a further embodiment, the topography measurement system 202 mayreceive a wafer 204 in a substantially vertical position and in asubstantially free state. For example, a finger gripper (e.g., threefinger gripper) may be implemented to receive and hold the wafer in avertical position. In this sense, the topography system 202 may collectdata from the wafer in an “unchucked” free state such that the shape ofa back surface of the wafer does not impact the shape of the frontsurface of the wafer.

The wafer shape may be quantified at a selected number of points andpositions across a surface of the wafer (e.g., front-side of wafer orback-side of wafer) at a first wafer process level (e.g., bare waferstate) and at an additional process level (e.g., first patterninglevel). In a general sense, the wafer may be quantified across a surfaceof the wafer at a process level N and at process level N+1. As notedpreviously herein, the topography system 202 may include aninterferometric based system, such as, but not limited to, a dual Fizeauinterferometer 220. Utilizing the dual Fizeau interferometry system 220of system 200, the dual interferometers of the system 220 maysimultaneously measure height variations of both the front-side surfaceand back-side surface of the wafer 204. A two-dimensional shape maps(x,y) may be constructed using the shape value calculated at each ofthe measured points utilizing the measured height variation at thosepoints and Eq. 1 (or an analog to Eq. 1). It is recognized herein thatthe computing system 206 may execute the calculation of the shape ateach of the grid of points of the wafer surface using Eq. 1 and thenform the shape map (e.g., numerical value plot map or a contrast map)using each of the calculated shape values. It is further recognized thatany number of methods may exist to measure shape of a wafer and themethodology described above should be interpreted as merely anillustration of one such method.

In an alternative embodiment, the values of the shape of a wafer inquestion may be received from a system other than the topography system202. Applicant notes that, while the above description has primarilydescribed the system 200 as including a topography system 200, thetopography measurements used in process 700 need not be performedcontemporaneously with the subsequent calculations of shape change,slope shape change, process tool correctables, and the like, asdiscussed in the remainder of the present disclosure. For example, theshape values may be received from a remote user (not shown). In anotherexample, the shape values may be retrieved from a memory (not shown) ofthe system 200.

In step 704, a wafer shape change value may be generated for each of thepoints of the set of points of step at the first process level (e.g.,level N) and the additional process level (e.g., level N+1) using theset of wafer shape values found in step 702. In this regard, the wafershape change value at each point corresponds to a change in wafer shapebetween the first process level and the second process level. In oneembodiment, the calculated wafer shape change values for each of thepoints may be used to form a two-dimensional (e.g., X-Y) shape changemap. It is noted herein that the wafer shape change value generated ateach point may include a front-side surface change or a back-sidesurface change.

In step 706, a set of slope of shape change values may be generated bycalculating a slope of shape change at each of the points utilizing thegenerated wafer shape change value at each of the points found in step704. In this regard, each of the slope of shape change valuescorresponds to a slope of the change in wafer shape along at least onedirection (e.g., X-direction or Y-direction) of the surface of the wafer204. In one embodiment, each of the slope of shape change values may becomputed using the shape change values of neighboring points of thetwo-dimensional map of step 704. In other embodiments, the set of slopeof shape change values may include a set of front-side surface changevalues or a set of back-side surface change values.

In step 708, a set of process tool correctable may be calculated. In oneaspect, the set of process tool correctables may be calculated utilizingthe set of slope of change values of step 706. In one embodiment, theset of process tool correctables may include wafer-level process toolcorrectables. In another embodiment, the set of process toolcorrectables may include field-level process tool correctables. In thecase of field level process tool correctables, the field size used incalculating the set of correctables is user-definable. It is furthernoted that the process tool correctable may be linear or higher-order.In the case of a wafer-level first order correction, the correctablesmay take the form:

dx=Δx−θ _(x) y _(wafer) +ΔM _(x) x _(wafer)  (Eq. 2)

dy=Δy+θ _(y) x _(wafer) +ΔM _(y) y _(wafer)  (Eq. 3)

where dx and dy represent the corrections in the x-direction andy-direction respectively, Δx and Δy represent the shift in x-directionand y-direction respectively, and ΔM_(x) and ΔM_(y) represent themagnification correction in the x-direction and y-directionrespectively. Moreover, in the case of field-level first ordercorrection, the correctables may take the form:

dx=Δx−θ _(x) y _(wafer) +ΔM _(x) x _(wafer)−φ_(x) y _(field) +Δm _(x) x_(field)  (Eq. 4)

dy=Δy+θ _(y) x _(wafer) +ΔM _(y) y _(wafer)+φ_(y) x _(field) +Δm _(y) y_(field)  (Eq. 5)

where φ_(x)y_(field) and φ_(y)x_(field) represent rotational field-levelterms and Δm_(x)x_(field) and Δm_(y)y_(field) represent magnificationfield-level correction terms. In step 710, a set of slope shape changeresiduals (SSCRs) may be generated by calculating a slope of shapechange residual value at each of the points utilizing the set of processtool correctables of step 708.

The calculation of wafer-level and field-level process tool correctablesas well as linear and higher-order process tool correctables and thegeneral calculation of residuals are described in U.S. Pat. No.7,876,438, issued on Jan. 25, 2011, which is incorporated herein byreference in the entirety.

In step 712, a plurality of metric analysis regions distributed acrossthe surface of the substrate may be defined. In one aspect, each metricanalysis region may encompass one or more points of the plurality ofpoints. In additional aspects, the size, frequency, and position of themetric analysis regions are user selectable. For example, a user mayselect each region to have a selected geometrical shape. For instance,at least some of the plurality of metric analysis regions may include arectangle, a radial band, or a radial sector. For example, the pluralityof metric analysis regions may consist of multiple concentric radialbands centered about the center of the wafer, with each band having aselected thickness along the radial direction. By way of anotherexample, the plurality of metric analysis regions may consist ofmultiple radial sectors distributed about the center of the wafer, witheach sector defined by a selected angle.

In another example, the plurality of metric analysis regions may consistof multiple rectangular regions distributed about the wafer in agrid-like manner, with each sector defined by a thickness in the X- andY-directions. In a further embodiment, the size and frequency of theregions may be selected based on field or die dimensions. For example, agiven region may have a size of approximately 25 mm by 10 mm,corresponding to the size of a specific lithographic site on the wafer.In this regard, it is noted that different regions of the plurality ofmetric analysis regions may different sizes, specified according to thesize of the integrated circuits in question.

In a further embodiment, step 712 may include forming 50 to 1000analysis regions distributed across the wafer surface. Applicant notesthat the above described geometrical arrangement for the metric analysisregions is not limiting and should be interpreted merely asillustrative. Those skilled in the art should recognize that the metricanalysis regions may be formed by a variety of geometrical shapes,arrangements, and frequency.

In step 714, one or more residual slope shape change metrics for eachmetric analysis region may be generated based on one or more SSCRswithin each metric analysis region. In this regard, the residual slopeshape change values encompassed by a given metric analysis region may beused to calculate a residual slope shape change metric for that region.In one embodiment, a residual slope shape change mean metric may begenerated for each region by calculating the mathematical mean for theresidual slope shape change values contained within each region. Inanother embodiment, a residual slope shape change median metric may begenerated for each region by finding the mathematical median for theresidual slope shape change values contained within each region. Inanother embodiment, a residual slope shape change max/min metric may begenerated for each region by finding the maximum or minimum residualslope shape change value of the set of residual slope shape changevalues contained within each region. In another embodiment, a residualslope shape change range metric may be generated for each region byfinding the range (e.g., difference between maximum and minimum) in theresidual slope shape change values contained within each region. Inanother embodiment, a residual slope shape change deviation metric maybe generated for each region by finding a deviation (e.g., standarddeviation) in a distribution of the residual slope shape change valuescontained within each region.

In a further embodiment, metric values from multiple regions may be usedto form a single global residual shape slope change wafer metric. Forexample, each of the mean metric values calculated for each of theanalysis regions may be combined to form a global mean metric value forthe entire wafer. By way of another example, a global range metric maybe formed utilizing two or more of the residual slope shape change meanmetrics found above. In one sense, the global range metric may bemeasured using the range in mean values obtained from each region. Inanother sense, the global range metric may be measured using thesmallest minimum metric found for the regions and the largest maximummetric found for the regions. In a general sense, any combination of themetrics obtained from the individual regions may be used to form aglobal residual slope shape change metric, thereby characterizing theresidual slope shape change at the wafer level.

In a further step, the process 700 may generate a contour map of theresidual slope shape change metrics found in step 714. For example, themetrics calculated in step 714 may be plotted on a two-dimensional grid,with the magnitude of each metric value associated with a selectedregion depicted along the “z-direction.” In another example, the metricscalculated in step 714 may be depicted as numerical values on atwo-dimensional map. In a further embodiment, the system 200 may presentthe contour map to a user via a display device (not shown). Utilizing auser interface device the user may identify excursion regions of thewafer. In turn, the user may flag one or more of the identify excursionregions found on the wafer and the system 200 may then controlsubsequent processes in those identified regions.

In a further step, the process 700 may generate one or more residualoverlay metrics for each metric analysis region based on one or moreresidual overlay values within each metric analysis region. In thisregard, the residual overlay values encompassed by a given metricanalysis region may be used to calculate a residual overlay metric forthat region. In one embodiment, a residual overlay mean metric may begenerated for each region by calculating the mathematical mean for theresidual overlay values contained within each region. In anotherembodiment, a residual overlay median metric may be generated for eachregion by finding the mathematical median for the residual overlayvalues contained within each region. In another embodiment, a residualoverlay max/min metric may be generated for each region by finding themaximum or minimum residual overlay value of the set of residual overlayvalues contained within each region. In another embodiment, a residualoverlay range metric may be generated for each region by finding therange (e.g., difference between maximum and minimum) in the residualoverlay values contained within each region. In another embodiment, aresidual overlay deviation metric may be generated for each region byfinding a deviation (e.g., standard deviation) in a distribution of theresidual overlay contained within each region.

In a further embodiment, metric values from multiple regions may be usedto form a single global residual overlay wafer metric. For example, eachof the mean metric values calculated for each of the analysis regionsmay be combined to form a global mean residual overlay metric value forthe entire wafer. By way of another example, a global range metric maybe formed utilizing two or more of the residual overlay mean metricsfound above. In one sense, the global range metric may be measured usingthe range in mean values obtained from each region. In another sense,the global range metric may be measured using the smallest minimummetric found for the regions and the largest maximum metric found forthe regions. In a general sense, any combination of the metrics obtainedfrom the individual regions may be used to form a global residualoverlay metric, thereby characterizing the residual overlay at the waferlevel.

FIG. 8 illustrates a process 800 providing a wafer geometry metricsuitable for implementation by system 200 of the present invention. Inone aspect, it is recognized that data processing steps of the processflow 800 may be carried out via a pre-programmed algorithm executed byone or more processors of the one or more computing systems 206. Whilethe following description is presented in the context of system 200, itis recognized herein that the particular structural aspects of system200 do not represent limitations and should be interpreted asillustrative only.

In step 802, a wafer shape value at each of a plurality of points of asurface of a wafer maybe acquired at a selected process level. It isnoted herein that the wafer shape values may be acquired in a mannersimilar to that described in step 702 of process flow 700 describedpreviously herein.

In step 804, a set of slope of shape values may be generated bycalculating a slope of shape at each of the points utilizing thegenerated wafer shape value at each of the points found in step 802. Inthis regard, each of the slope of shape values corresponds to a slope ofthe wafer shape along at least one direction (e.g., X-direction orY-direction) of the surface of the wafer 204. In one embodiment, each ofthe slope of shape values may be computed using the shape values ofneighboring points of a two-dimensional map formed using the wafer shapevalues acquired in step 802. It is noted herein that the wafer shapeslope values generated at each point may include a front-side surfaceshape slope or a back-side surface shape slope.

In step 806, a set of process tool correctable may be calculated. In oneaspect, the set of process tool correctables may be calculated utilizingthe set of slope of shape values of step 804. As in process flow 700,the set of process tool correctables may include wafer-level processtool correctables or field-level process tool correctables. It is notedherein that the calculation of process tool correctables is similar tothat described in process flow 700. As such, the description of processtool correctable calculation of process 700 should be interpreted toextend to step 806 of process 800. In step 808, a set of slope shaperesiduals (SSRs) may be generated by calculating a slope of shaperesidual value at each of the points utilizing the set of process toolcorrectables of step 806. In step 810, a plurality of metric analysisregions distributed across the surface of the substrate may be defined.In step 812, one or more residual slope shape metrics for each metricanalysis region may be generated based on one or more SSRs within eachmetric analysis region. It is noted herein that steps 808-812 areanalogous to steps 710-714 of process flow 700. As such, the descriptionof steps 710-714 should be interpreted to extend to the process steps808-812 of process flow 800.

FIG. 9A illustrates a process 900 for sorting wafers utilizing a slopeof shape metric suitable for implementation by system 200 of the presentinvention. In one aspect, it is recognized that data processing steps ofthe process flow 900 may be carried out via a pre-programmed algorithmexecuted by one or more processors of the one or more computing systems206. While the following description is presented in the context ofsystem 200, it is recognized herein that the particular structuralaspects of system 200 do not represent limitations and should beinterpreted as illustrative only.

In step 902, a set of wafers may be received by the system 200. Forexample, a set of bare wafers may be received by the system 200. In step904, a set of wafer shape values from a surface of each wafer at aselected process level (e.g., bare wafer process level) may be acquired.In step 906, a set of residual slope shape metrics for each wafer may begenerated by calculating a residual slope shape metric at each of aplurality of points of each wafer. It is noted herein that the wafershape slope values generated at each point may include a front-sidesurface shape slope or a back-side surface shape slope. It is furthernoted that the steps 902 through 906 are previously described throughoutthe present disclosure. For example, the residual slope shape metricsgenerated in process flow 800 may be interpreted to extend to steps offinding a set of residual slope shape metrics for each of the wafers ofprocess 900.

In step 908, a neutral surface 952 for each wafer in a chucked state maybe determined. In step 910, a neutral surface factor (NSF) for eachwafer utilizing the determined neutral surface for each wafer and aplurality of positions associated with a plurality of patterns of eachwafer may be calculated. FIG. 9B depicts a conceptual illustration 950of a neutral surface 952 and a corresponding neutral surface factor. Inone embodiment, the neutral surface factor 954 may be interpreted as thedistance between the neutral surface and a pattern surface on the wafer,wherein multiple pattern features 956 are disposed. The in-planedistortions created by the change in wafer shape give rise to patternplace errors 958. Pattern placement errors may be derived based on theNSF 954 and the local slope of the back-side surface at each of a set ofpoints and the corresponding slope map of the back-side surface 960.Neutral surface, neutral surface factor, and the calculation of patternplace errors (or “image place error) are discussed in detail in PradeepVukkadala, “Correction Strategies to Compensate for Image PlacementErrors Induced during EUVL Mask Chucking,” The University ofWisconsin—Madison Dissertations Et Theses, ProQuest Dissertations EtTheses, ISBN 9781124367644 (2010).

In step 912, a set of pattern placement error (PPE) residual values foreach wafer may be determined, the PPE residual value for each point foreach wafer being a product of at least the calculated NSF for eachwafer, the residual slope shape metric for the point, and a thickness ofthe wafer. In this regard, the pattern placement error residual valuefor each point may be represented by:

PPE_(residual)=NSF×SlopeShape_(residual) ×t _(s)  (Eq. 6)

where NSF is the neutral surface factor, SlopeShape_(residual) is theslope of shape residual value (or slope of shape residual metric) forthe given point, as determined through any of the various mannersdescribed through the present disclosure, and t_(s) is the thickness ofthe wafer.

In step 914, a threshold for the set of residual shape metrics suitablefor maintaining the set of PPE residuals below a selected level may bedetermined. In this regard, a PPE residual value required for a givenprocess or application may be selected. In this sense, the system 200 oruser may determine the required PPE residual specification needed forthe given device. In turn, a threshold for the residual shape metricsmay be determined that will maintain or surpass the selected PPEresidual level. In this regard, equation 6 correlates the PPE residualvalues to the slope of shape residual values, and utilizing thisrelationship it may be determined what threshold shape residual valuesare needed in order to meet the requirements for the PPE residuals,which are dictated by the given process or device.

In step 916, the plurality of wafers may be characterized by comparingthe determined threshold for the set of residual shape metrics to thegenerated set of residual slope shape metrics for each wafer. In afurther embodiment, the set of wafers may be sorted by comparing thedetermined one or more thresholds for the set of residual shape metricsto the generated set of residual slope shape metrics for each wafer. Inthis regard, each wafer of the set of wafers may be binned according tothe set of residual shape metrics associated with the given wafer.

In another embodiment, each of the set of wafers may be monitored bycomparing the determined one or more thresholds for the set of residualshape metrics to the generated set of residual slope shape metrics foreach wafer. In response to the monitoring of the plurality of wafers,one or more processes may be modified in order to maintain the generatedset of residual slope shape metrics for each wafer below the one or morethresholds. In an additional embodiment, in response to the monitoringof the plurality of wafers, one or more processes may be developed inorder to establish the generated set of residual slope shape metrics foreach wafer below the one or more thresholds.

FIG. 10 illustrates a process 1000 for process uniformity controlutilizing a slope of shape change metric suitable for implementation bysystem 200 of the present invention. In one aspect, it is recognizedthat data processing steps of the process flow 1000 may be carried outvia a pre-programmed algorithm executed by one or more processors of theone or more computing systems 206. While the following description ispresented in the context of system 200, it is recognized herein that theparticular structural aspects of system 200 do not represent limitationsand should be interpreted as illustrative only.

In step 1002, a wafer shape value at each of a plurality of points of asurface of a wafer at a first process level and an additional processlevel may be acquired. In step 1004, a wafer shape change value at eachof the points utilizing the acquired wafer shape value at each of thepoints at the first process level and the additional process level maybe generated, the wafer shape change value at each point correspondingto a change in wafer shape between the first process level and thesecond process level. In step 1006, one or more residual slope shapechange metrics may be generated utilizing the generated wafer shapechange value at each of the points. In step 1008, process control to oneor more process tools may be provided based on the generated one or moreresidual slope shape change metrics. In this regard, the monitoring ofthe slope shape change metrics associated with two or more process(e.g., N and N+1) may be used to control one or more processes. Thegiven process tool may receive feedback from the computing system 206and, in response to this feedback, the process tool may make adjustmentsso that the given process creates a wafer shape change (as measured viaone of the described slope shape change metrics) that falls within arequired specification. The slope shape change metrics may be used tocontrol any process known in the art, such as, but not limited to, CMP,RTP, etching, and film deposition.

FIG. 11 illustrates a process 1100 for process uniformity controlutilizing a slope of shape change metric suitable for implementation bysystem 200 of the present invention. In one aspect, it is recognizedthat data processing steps of the process flow 1100 may be carried outvia a pre-programmed algorithm executed by one or more processors of theone or more computing systems 206. While the following description ispresented in the context of system 200, it is recognized herein that theparticular structural aspects of system 200 do not represent limitationsand should be interpreted as illustrative only.

In step 1102, a wafer shape value at each of a plurality of points of asurface of a wafer may be acquired at a first process level and anadditional process level. In step 1104, a set of wafer shape changevalues may be generated by calculating a wafer shape change value ateach of the points utilizing the acquired wafer shape value at each ofthe points at the first process level and the additional process level.In step 1106, a set of slope shape change residuals may be generatedutilizing the generated wafer shape change value at each of the points.In step 1108, a set of residual slope shape change metrics may becalculated utilizing the set of sloe shape change residuals.

In step 1110, a set of overlay values may be acquired at a plurality ofpoints on the surface of the wafer at the additional process level, theset of overlay values associated with a misalignment produced betweenthe first process level and the additional process level. In step 1112,a set of overlay residuals may be generated utilizing the acquired setof overlay values. In step 1114, a set of overlay residual metrics maybe calculated utilizing the set of overlay residuals.

In step 1116, a calibration curve may be generated by comparing the setof residual slope shape change metrics to the set of residual overlaymetrics. FIG. 12 illustrates one such calibration curve, whereby overlayresiduals obtained from a wafer are related to a set of wafer slopeshape change residuals also obtained from the wafer. It is noted hereinthat the curve may consist of a known fitting function (e.g., polynomialexpansion) fitted to the overlay residual metrics versus slope of shapechange residual metrics data 1200. In this regard, the calibration curveallows the system 200 or user to determine the value of the wafer slopeshape change residuals needed to attain a selected overlay residualvalue. In step 1118, a threshold may be determined for the set ofresidual slope shape change metrics suitable for maintaining residualoverlay below a selected level based on the generated calibration curve.As shown in FIG. 12, the wafer slope of shape residual value needed toachieve an overlay residual value at or below 3 nm is demarked by line1206. In a further embodiment, a plurality of wafers may be sorted bygenerating a set of residual slope shape change metrics for each of thewafers and comparing the acquired set of residual slope shape changemetrics to the threshold determined above.

All of the methods described herein may include storing results of oneor more steps of the method embodiments in a storage medium. The resultsmay include any of the results described herein and may be stored in anymanner known in the art. The storage medium may include any storagemedium described herein or any other suitable storage medium known inthe art. After the results have been stored, the results can be accessedin the storage medium and used by any of the method or systemembodiments described herein, formatted for display to a user, used byanother software module, method, or system, etc. Furthermore, theresults may be stored “permanently,” “semi-permanently,” temporarily, orfor some period of time. For example, the storage medium may be randomaccess memory (RAM), and the results may not necessarily persistindefinitely in the storage medium.

It is further contemplated that each of the embodiments of the methoddescribed above may include any other step(s) of any other method(s)described herein. In addition, each of the embodiments of the methoddescribed above may be performed by any of the systems described herein.

Those having skill in the art will appreciate that there are variousvehicles by which processes and/or systems and/or other technologiesdescribed herein can be effected (e.g., hardware, software, and/orfirmware), and that the preferred vehicle will vary with the context inwhich the processes and/or systems and/or other technologies aredeployed. For example, if an implementer determines that speed andaccuracy are paramount, the implementer may opt for a mainly hardwareand/or firmware vehicle; alternatively, if flexibility is paramount, theimplementer may opt for a mainly software implementation; or, yet againalternatively, the implementer may opt for some combination of hardware,software, and/or firmware. Hence, there are several possible vehicles bywhich the processes and/or devices and/or other technologies describedherein may be effected, none of which is inherently superior to theother in that any vehicle to be utilized is a choice dependent upon thecontext in which the vehicle will be deployed and the specific concerns(e.g., speed, flexibility, or predictability) of the implementer, any ofwhich may vary. Those skilled in the art will recognize that opticalaspects of implementations will typically employ optically-orientedhardware, software, and or firmware.

Those skilled in the art will recognize that it is common within the artto describe devices and/or processes in the fashion set forth herein,and thereafter use engineering practices to integrate such describeddevices and/or processes into data processing systems. That is, at leasta portion of the devices and/or processes described herein can beintegrated into a data processing system via a reasonable amount ofexperimentation. Those having skill in the art will recognize that atypical data processing system generally includes one or more of asystem unit housing, a video display device, a memory such as volatileand non-volatile memory, processors such as microprocessors and digitalsignal processors, computational entities such as operating systems,drivers, graphical user interfaces, and applications programs, one ormore interaction devices, such as a touch pad or screen, and/or controlsystems including feedback loops and control motors (e.g., feedback forsensing position and/or velocity; control motors for moving and/oradjusting components and/or quantities). A typical data processingsystem may be implemented utilizing any suitable commercially availablecomponents, such as those typically found in datacomputing/communication and/or network computing/communication systems.

The herein described subject matter sometimes illustrates differentcomponents contained within, or connected with, different othercomponents. It is to be understood that such depicted architectures aremerely exemplary, and that in fact many other architectures can beimplemented which achieve the same functionality. In a conceptual sense,any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “connected”, or “coupled”, toeach other to achieve the desired functionality, and any two componentscapable of being so associated can also be viewed as being “couplable”,to each other to achieve the desired functionality. Specific examples ofcouplable include but are not limited to physically mateable and/orphysically interacting components and/or wirelessly interactable and/orwirelessly interacting components and/or logically interacting and/orlogically interactable components.

While particular aspects of the present subject matter described hereinhave been shown and described, it will be apparent to those skilled inthe art that, based upon the teachings herein, changes and modificationsmay be made without departing from the subject matter described hereinand its broader aspects and, therefore, the appended claims are toencompass within their scope all such changes and modifications as arewithin the true spirit and scope of the subject matter described herein.

Furthermore, it is to be understood that the invention is defined by theappended claims.

Although particular embodiments of this invention have been illustrated,it is apparent that various modifications and embodiments of theinvention may be made by those skilled in the art without departing fromthe scope and spirit of the foregoing disclosure. Accordingly, the scopeof the invention should be limited only by the claims appended hereto.

It is believed that the present disclosure and many of its attendantadvantages will be understood by the foregoing description, and it willbe apparent that various changes may be made in the form, constructionand arrangement of the components without departing from the disclosedsubject matter or without sacrificing all of its material advantages.The form described is merely explanatory, and it is the intention of thefollowing claims to encompass and include such changes.

What is claimed:
 1. A method for sorting wafers utilizing a slope ofshape metric, comprising: receiving a plurality of wafers; acquiring aset of wafer shape values from a surface of each wafer at a selectedprocess level; generating a set of residual slope shape metrics for eachwafer by calculating a residual slope shape metric at each of aplurality of points of each wafer; determining a neutral surface of eachwafer in a chucked state; calculating a neutral surface factor (NSF) foreach wafer utilizing the determined neutral surface for each wafer and aplurality of positions associated with a plurality of patterns of eachwafer; determining a set of pattern placement error (PPE) residualvalues for each wafer, the PPE residual value for each point for eachwafer being a product of at least the calculated NSF for each wafer, theresidual slope shape metric for the point, and a thickness of the wafer;determining one or more thresholds for the set of residual shape metricssuitable for maintaining the set of PPE residuals below one or moreselected levels; and characterizing the plurality of wafers by comparingthe determined one or more thresholds for the set of residual shapemetrics to the generated set of residual slope shape metrics for eachwafer.
 2. The method of claim 1, wherein the NSF is a distance betweenthe neutral surface and a pattern surface of the wafer.
 3. The method ofclaim 1, wherein the selected process level is a bare wafer processlevel.
 4. The method of claim 1, wherein the characterizing theplurality of wafers by comparing the determined one or more thresholdsfor the set of residual shape metrics to the generated set of residualslope shape metrics for each wafer comprises: sorting the plurality ofwafers by comparing the determined one or more thresholds for the set ofresidual shape metrics to the generated set of residual slope shapemetrics for each wafer.
 5. The method of claim 1, wherein the sortingthe plurality of wafers by comparing the determined one or morethresholds for the set of residual shape metrics to the generated set ofresidual slope shape metrics for each wafer comprises: binning eachwafer according to a comparison between the set of residual shapemetrics associated with the wafer and the determined threshold.
 6. Themethod of claim 1, wherein the characterizing the plurality of wafers bycomparing the determined one or more thresholds for the set of residualshape metrics to the generated set of residual slope shape metrics foreach wafer comprises: monitoring each of plurality of wafers bycomparing the determined one or more thresholds for the set of residualshape metrics to the generated set of residual slope shape metrics foreach wafer.
 7. The method of claim 6, further comprising: responsive tothe monitoring of each of the plurality of wafers, modifying one or moreprocesses in order to maintain the generated set of residual slope shapemetrics for each wafer below the one or more thresholds.
 8. The methodof claim 6, further comprising: responsive to the monitoring of each ofthe plurality of wafers, identifying one or more processes in order toestablish the generated set of residual slope shape metrics for eachwafer below the one or more thresholds.
 9. A method for processuniformity control, comprising: acquiring a wafer shape value at each ofa plurality of points of a surface of a wafer at a first process leveland an additional process level; generating a wafer shape change valueat each of the points utilizing the acquired wafer shape value at eachof the points at the first process level and the additional processlevel, the wafer shape change value at each point corresponding to achange in wafer shape between the first process level and the secondprocess level generating one or more residual slope shape change metricsutilizing the generated wafer shape change value at each of the points;and providing process control to one or more process tools based on thegenerated one or more residual slope shape change metrics.
 10. Themethod of claim 9, wherein the generated wafer shape change value ateach of the points comprises: at least one of a front-side wafer surfaceshape change or a back-side wafer surface shape change.
 11. A method foroverlay control, comprising: acquiring a wafer shape value at each of aplurality of points of a surface of a wafer at a first process level andan additional process level; generating a set of wafer shape changevalues by calculating a wafer shape change value at each of the pointsutilizing the acquired wafer shape value at each of the points at thefirst process level and the additional process level; generating a setof slope shape change residuals utilizing the generated wafer shapechange value at each of the points; calculating a set of residual slopeshape change metrics utilizing the set of sloe shape change residuals;acquiring a set of overlay values at a plurality of points on thesurface of the wafer at the additional process level, the set of overlayvalues associated with a misalignment produced between the first processlevel and the additional process level; generating a set of overlayresiduals utilizing the acquired set of overlay values; calculating aset of overlay residual metrics utilizing the set of overlay residuals;generating a calibration curve by comparing the set of residual slopeshape change metrics to the set of residual overlay metrics; anddetermining a threshold for the set of residual slope shape changemetrics suitable for maintaining residual overlay below a selected levelbased on the generated calibration curve.
 12. The method of claim 11,further comprising: sorting a plurality of wafers by generating a set ofresidual slope shape change metrics for each of the wafers and comparingthe acquired set of residual slope shape change metrics to thedetermined threshold.
 13. The method of claim 11, wherein the generatedwafer shape change value at each of the points comprises: at least oneof a front-side wafer surface shape change or a back-side wafer surfaceshape change.
 14. A system for sorting wafers utilizing a slope of shapemetric, comprising: a topography system configured to perform a set oftopography measurements in order to acquire a set of wafer shape values,at a selected process level, from a surface of each wafer of a pluralityof wafers; and one or more computing systems communicatively coupled tothe topography and configured to receive the set of topographymeasurements, the one or more computing systems further configured to:generate a set of residual slope shape metrics for each wafer bycalculating a residual slope shape metric at each of a plurality ofpoints of each wafer; determine a neutral surface of each wafer in achucked state; calculate a neutral surface factor (NSF) for each waferutilizing the determined neutral surface for each wafer and a pluralityof positions associated with a plurality of patterns of each wafer;determine a set of pattern placement error (PPE) residual values foreach wafer, the PPE residual value for each point for each wafer being aproduct of at least the calculated NSF for each wafer, the residualslope shape metric for the point, and a thickness of the wafer;determine one or more thresholds for the set of residual shape metricssuitable for maintaining the set of PPE residuals below one or moreselected levels; and characterize the plurality of wafers by comparingthe determined one or more thresholds for the set of residual shapemetrics to the generated set of residual slope shape metrics for eachwafer.
 15. The system of claim 14, wherein the topography systemscomprises: an interferometry based topography system.
 16. The system ofclaim 14, wherein the interferometry based topography system comprises:a dual Fizeau interferometer.
 17. The system of claim 14, wherein thetopography systems comprises: a topography system configured to measurea front-side surface of the wafer and the back-side surface of the wafersimultaneously.
 18. A system for process uniformity control, comprising:a topography system configured to perform a set of topographymeasurements in order to acquire a wafer shape value at each of aplurality of points of a surface of a wafer at a first process level andan additional process level; and one or more computing systemscommunicatively coupled to the topography and configured to receive theset of topography measurements, the one or more computing systemsfurther configured to: generate a wafer shape change value at each ofthe points utilizing the acquired wafer shape value at each of thepoints at the first process level and the additional process level, thewafer shape change value at each point corresponding to a change inwafer shape between the first process level and the second process levelgenerate one or more residual slope shape change metrics utilizing thegenerated wafer shape change value at each of the points; and provideprocess control to one or more process tools based on the generated oneor more residual slope shape change metrics.
 19. A system for overlaycontrol, comprising: a topography system configured to perform a set oftopography measurements in order to acquire a wafer shape value at eachof a plurality of points of a surface of a wafer at a first processlevel and an additional process level; and one or more computing systemscommunicatively coupled to the topography and configured to receive theset of topography measurements, the one or more computing systemsfurther configured to: generate a set of wafer shape change values bycalculating a wafer shape change value at each of the points utilizingthe acquired wafer shape value at each of the points at the firstprocess level and the additional process level; generate a set of slopeshape change residuals utilizing the generated wafer shape change valueat each of the points; calculate a set of residual slope shape changemetrics utilizing the set of sloe shape change residuals; acquire a setof overlay values at a plurality of points on the surface of the waferat the additional process level, the set of overlay values associatedwith a misalignment produced between the first process level and theadditional process level; generate a set of overlay residuals utilizingthe acquired set of overlay values; calculate a set of overlay residualmetrics utilizing the set of overlay residuals; generate a calibrationcurve by comparing the set of residual slope shape change metrics to theset of residual overlay metrics; and determine a threshold for the setof residual slope shape change metrics suitable for maintaining residualoverlay below a selected level based on the generated calibration curve.